$scope object is basically used to glue together the view and the controller of your angular application. 
It does not make much sense to pass it into a service.
Services are singleton objects used to share data among several controllers,directives,filters etc.
Some changes need to be made in your code :
1. Instead of using $scope in service used it in controller.
2. Return the object from the service and get it into the controller inside a $scope object.
Based on the approach described above, you can change your code like this :
controller :
var testModule = angular.module('testmodule', [])
.controller('ctrl', function ($scope, mser) {
  $scope.as = mser.aa();
})
.service('mser', function() {
  this.aa = function(){
    return "hello mars";
}});
view :
<span>{{::as}}</span>